Flow and diffusion in channel-guided cell migration

Using a probabilistic approach to derive a two-phase model of flow-induced cell migration

Interstitial fluid flow is a feature of many solid tumors. In vitro experiments have shown that such fluid flow can direct tumor cell movement upstream or downstream depending on the balance between the competing mechanisms of tensotaxis (cell migration up stress gradients) and autologous chemotaxis (downstream cell movement in response to flow-induced gradients of self-secreted chemoattractants). In this work we develop a probabilistic-continuum, two-phase model for cell migration in response to interstitial flow. We use a kinetic description for the cell velocity probability density function, and model the flow-dependent mechanical and chemical stimuli as forcing terms that bias cell migration upstream and downstream. Using velocity-space averaging, we reformulate the model as a system of continuum equations for the spatiotemporal evolution of the cell volume fraction and flux in response to forcing terms that depend on the local direction and magnitude of the mechanochemical cues. We specialize our model to describe a one-dimensional cell layer subject to fluid flow. Using a combination of numerical simulations and asymptotic analysis, we delineate the parameter regime where transitions from downstream to upstream cell migration occur. As has been observed experimentally, the model predicts downstream-oriented chemotactic migration at low cell volume fractions, and upstream-oriented tensotactic migration at larger volume fractions. We show that the locus of the critical volume fraction, at which the system transitions from downstream to upstream migration, is dominated by the ratio of the rate of chemokine secretion and advection. Our model also predicts that, because the tensotactic stimulus depends strongly on the cell volume fraction, upstream, tensotaxis-dominated migration occurs only transiently when the cells are initially seeded, and transitions to downstream, chemotaxis-dominated migration occur at later times due to the dispersive effect of cell diffusion.

A simple agent-based hybrid model to simulate the biophysics of glioblastoma multiforme cells and the concomitant evolution of the oxygen field

BACKGROUND AND OBJECTIVES

Glioblastoma multiforme (GBM) is one of the most aggressive cancers of the central nervous system. It is characterized by a high mitotic activity and an infiltrative ability of the glioma cells, neovascularization and necrosis. GBM evolution entails the continuous interplay between heterogeneous cell populations, chemotaxis, and physical cues through different scales. In this work, an agent-based hybrid model is proposed to simulate the coupling of the multiscale biological events involved in the GBM invasion, specifically the individual and collective migration of GBM cells and the concurrent evolution of the oxygen field and phenotypic plasticity. An asset of the formulation is that it is conceptually and computationally simple but allows to reproduce the complexity and the progression of the GBM micro-environment at cell and tissue scales simultaneously.

METHODS

The migration is reproduced as the result of the interaction between every single cell and its micro-environment. The behavior of each individual cell is formulated through genotypic variables whereas the cell micro-environment is modeled in terms of the oxygen concentration and the cell density surrounding each cell. The collective behavior is formulated at a cellular scale through a flocking model. The phenotypic plasticity of the cells is induced by the micro-environment conditions, considering five phenotypes.

RESULTS

The model has been contrasted by benchmark problems and experimental tests showing the ability to reproduce different scenarios of glioma cell migration. In all cases, the individual and collective cell migration and the coupled evolution of both the oxygen field and phenotypic plasticity have been properly simulated. This simple formulation allows to mimic the formation of relevant hallmarks of glioblastoma multiforme, such as the necrotic cores, and to reproduce experimental evidences related to the mitotic activity in pseudopalisades.

CONCLUSIONS

In the collective migration, the survival of the clusters prevails at the expense of cell mitosis, regardless of the size of the groups, which delays the formation of necrotic foci and reduces the rate of oxygen consumption.

The mechanical influence of densification on epithelial architecture

Epithelial tissues are the most abundant tissue type in animals, lining body cavities and generating compartment barriers. The function of a monolayered epithelial tissue-whether protective, secretory, absorptive, or filtrative-relies on the side-by-side arrangement of its component cells. The mechanical parameters that determine the shape of epithelial cells in the apical-basal plane are not well-understood. Epithelial tissue architecture in culture is intimately connected to cell density, and cultured layers transition between architectures as they proliferate. This prompted us to ask to what extent epithelial architecture emerges from two mechanical considerations: A) the constraints of densification and B) cell-cell adhesion, a hallmark feature of epithelial cells. To address these questions, we developed a novel polyline cell-based computational model and used it to make theoretical predictions about epithelial architecture upon changes to density and cell-cell adhesion. We tested these predictions using cultured cell experiments. Our results show that the appearance of extended lateral cell-cell borders in culture arises as a consequence of crowding-independent of cell-cell adhesion. However, cadherin-mediated cell-cell adhesion is associated with a novel architectural transition. Our results suggest that this transition represents the initial appearance of a distinctive epithelial architecture. Together our work reveals the distinct mechanical roles of densification and adhesion to epithelial layer formation and provides a novel theoretical framework to understand the less well-studied apical-basal plane of epithelial tissues.

A toolbox to analyze collective cell migration, proliferation and cellular organization simultaneously

BACKGROUND

Analyses of collective cell migration and orientation phenomena are needed to assess the behavior of multicellular clusters. While some tools to the authors' knowledge none is capable to analyze collective migration, cellular orientation and proliferation in phase contrast images simultaneously.

METHODS

We provide a tool based to analyze phase contrast images of dense cell layers. PIV is used to calculatevelocity fields, while the structure tensor provides cellular orientation. An artificial neural network is used to identify cell division events, allowing to correlate migratory and organizational phenomena with cell density.

CONCLUSION

The presented tool allows the simultaneous analysis of collective cell behavior from phase contrast images in terms of migration, (self-)organization and proliferation.

Morphology as indicator of adaptive changes of model tissues in osmotically and chemically changing environments

We investigate the formation and maintenance of the homeostatic state in the case of 2D epithelial tissues following an induction of hyperosmotic conditions, using media enriched with 80 to 320 mOsm of mannitol, NaCl, and urea. We characterise the changes in the tissue immediately after the osmotic shock, and follow it until the new homeostatic state is formed. We characterise changes in cooperative motility and proliferation pressure in the tissue upon treatment with the help of a theoretical model based on the delayed Fisher-Kolmogorov formalism, where the delay in density evolution is induced by the the finite time of the cell division. Finally we explore the adaptation of the homeostatic tissue to highly elevated osmotic conditions by evaluating the morphology and topology of cells after 20 days in incubation. We find that hyperosmotic environments together with changes in the extracellular matrix induce different mechanical states in viable tissues, where only some remain functional. The perspective is a relation between tissue topology and function, which could be explored beyond the scope of this manuscript. Experimental investigation of morphological effect of change of osmotic conditions on long-term tissue morphology and topology Effect of osmotic changes on transient tissue growth behaviour Analysis of recovery process of tissues post-osmotic-shock Toxicity limits of osmolytes in mid- to long-term tissue evolution Tissue adaptation to physiological changes in environment Long-term tissue stabilisation under altered osmotic conditions.

Matrix Anisotropy Promotes a Transition of Collective to Disseminated Cell Migration via a Collective Vortex Motion

Cells detached and disseminated away from collectively migrating cells are frequently found during tumor invasion at the invasion front, where extracellular matrix (ECM) fibers are parallel to the cell migration direction. However, it remains unclear how anisotropic topography promotes the transition of collective to disseminated cell migration. This study applies a collective cell migration model with and without 800 nm wide aligned nanogrooves parallel, perpendicular, or diagonal to the cell migration direction. After 120 hour migration, MCF7-GFP-H2B-mCherry breast cancer cells display more disseminated cells at the migration front on parallel topography than on other topographies. Notably, a fluid-like collective motion with high vorticity is enhanced at the migration front on parallel topography. Furthermore, high vorticity but not velocity is correlated with disseminated cell numbers on parallel topography. Enhanced collective vortex motion colocalizes with cell monolayer defects where cells extend protrusions into the free space, suggesting that topography-driven cell crawling for defect closure promotes the collective vortex motion. In addition, elongated cell morphology and frequent protrusions induced by topography may further contribute to the collective vortex motion. Overall, a high-vorticity collective motion at the migration front promoted by parallel topography suggests a cause of the transition of collective to disseminated cell migration.

The Mechanical Influence of Densification on Initial Epithelial Architecture

Epithelial tissues are the most abundant tissue type in animals, lining body cavities and generating compartment barriers. The function of a monolayer epithelium - whether protective, secretory, absorptive, or filtrative -relies on regular tissue architecture with respect to the apical-basal axis. Using an unbiased 3D analysis pipeline developed in our lab, we previously showed that epithelial tissue architectures in culture can be divided into distinct developmental categories, and that these are intimately connected to cell density: at sparse densities, cultured epithelial cell layers have a squamous morphology (Immature); at intermediate densities, these layers develop lateral cell-cell borders and rounded cell apices (Intermediate); cells at the highest densities reach their full height and demonstrate flattened apices (Mature). These observations prompted us to ask whether epithelial architecture emerges from the mechanical constraints of densification, and to what extent a hallmark feature of epithelial cells, namely cell-cell adhesion, contributes. In other words, to what extent is the shape of cells in an epithelial layer a simple matter of sticky, deformable objects squeezing together? We addressed this problem using a combination of computational modeling and experimental manipulations. Our results show that the first morphological transition, from Immature to Intermediate, can be explained simply by cell crowding. Additionally, we identify a new division (and thus transition) within the Intermediate category, and find that this second morphology relies on cell-cell adhesion.

Transitions in density, pressure, and effective temperature drive collective cell migration into confining environments

Epithelial cell collectives migrate through tissue interfaces and crevices to orchestrate processes of development, tumor invasion, and wound healing. Naturally, traversal of cell collective through confining environments involves crowding due to the narrowing space, which seems tenuous given the conventional inverse relationship between cell density and migration. However, physical transitions required to overcome such epithelial densification for migration across confinements remain unclear. Here, in contiguous microchannels, we show that epithelial (MCF10A) monolayers accumulate higher cell density before entering narrower channels; however, overexpression of breast cancer oncogene +ErbB2 reduced this need for density accumulation across confinement. While wildtype MCF10A cells migrated faster in narrow channels, this confinement sensitivity reduced after +ErbB2 mutation or with constitutively-active RhoA. The migrating collective developed pressure differentials upon encountering microchannels, like fluid flow into narrowing spaces, and this pressure dropped with their continued migration. These transitions of pressure and density altered cell shapes and increased effective temperature, estimated by treating cells as granular thermodynamic system. While +RhoA cells and those in confined regions were effectively warmer, cancer-like +ErbB2 cells remained cooler. Epithelial reinforcement by metformin treatment increased density and temperature differentials across confinement, indicating that higher cell cohesion could reduce unjamming. Our results provide experimental evidence for previously proposed theories of inverse relationship between density and motility-related effective temperature. Indeed, we show across cell lines that confinement increases pressure and effective temperature, which enable migration by reducing density. This physical interpretation of collective cell migration as granular matter could advance our understanding of complex living systems.

3D bioprinted colorectal cancer models based on hyaluronic acid and signalling glycans

In cancer microenvironment, aberrant glycosylation events of ECM proteins and cell surface receptors occur. We developed a protocol to generate 3D bioprinted models of colorectal cancer (CRC) crosslinking hyaluronic acid and gelatin functionalized with three signalling glycans characterized in CRC, 3'-Sialylgalactose, 6'-Sialylgalactose and 2'-Fucosylgalactose. The crosslinking, performed exploiting azide functionalized gelatin and hyaluronic acid and 4arm-PEG-dibenzocyclooctyne, resulted in biocompatible hydrogels that were 3D bioprinted with commercial CRC cells HT-29 and patient derived CRC tumoroids. The glycosylated hydrogels showed good 3D printability, biocompatibility and stability over the time. SEM and synchrotron radiation SAXS/WAXS analysis revealed the influence of glycosylation in the construct morphology, whereas MALDI-MS imaging showed that protein profiles of tumoroid cells vary with glycosylation, indicating that sialylation and fucosylation of ECM proteins induce diverse alterations to the proteome of the tumoroid and surrounding cells.

Collective rotational motion of freely expanding T84 epithelial cell colonies

Coordinated rotational motion is an intriguing, yet still elusive mode of collective cell migration, which is relevant in pathological and morphogenetic processes. Most of the studies on this topic have been carried out on epithelial cells plated on micropatterned substrates, where cell motion is confined in regions of well-defined shapes coated with extracellular matrix adhesive proteins. The driver of collective rotation in such conditions has not been clearly elucidated, although it has been speculated that spatial confinement can play an essential role in triggering cell rotation. Here, we study the growth of epithelial cell colonies freely expanding (i.e. with no physical constraints) on the surface of cell culture plates and focus on collective cell rotation in such conditions, a case which has received scarce attention in the literature. One of the main findings of our work is that coordinated cell rotation spontaneously occurs in cell clusters in the free growth regime, thus implying that cell confinement is not necessary to elicit collective rotation as previously suggested. The extent of collective rotation was size and shape dependent: a highly coordinated disc-like rotation was found in small cell clusters with a round shape, while collective rotation was suppressed in large irregular cell clusters generated by merging of different clusters in the course of their growth. The angular motion was persistent in the same direction, although clockwise and anticlockwise rotations were equally likely to occur among different cell clusters. Radial cell velocity was quite low as compared to the angular velocity, in agreement with the free expansion regime where cluster growth is essentially governed by cell proliferation. A clear difference in morphology was observed between cells at the periphery and the ones in the core of the clusters, the former being more elongated and spread out as compared to the latter. Overall, our results, to our knowledge, provide the first quantitative and systematic evidence that coordinated cell rotation does not require a spatial confinement and occurs spontaneously in freely expanding epithelial cell colonies, possibly as a mechanism for the system.

Dominant geometrical factors of collective cell migration in flexible 3D gelatin tube structures

Collective cell migration is a dynamic and interactive behavior of cell cohorts essential for diverse physiological developments in living organisms. Recent studies have revealed the importance of three-dimensional (3D) topographical confinements to regulate the migration modes of cell cohorts in tubular confinement. However, conventional in vitro assays fail to observe cells' behavior in response to 3D structural changes, which is necessary for examining the geometric regulation factors of collective migration. Here, we introduce a newly developed assay for fabricating flexible 3D structures of capillary microtunnels to examine the behavior of vascular endothelial cells (ECs) as they progress through the successive transition across wide or narrow tube structures. The microtunnels with altered diameters were formed inside gelatin-gel blocks by photo-thermal etching with micrometer-sized spot heating of the focused infrared laser absorption. The ECs migrated and spread two-dimensionally on the inner surface of gelatin capillary microtunnels as a monolayer instead of filling the entire capillary. In the straight cylindrical topographical constraint, leading ECs exhibited no apparent diameter dependence for the maximum peak migration velocity. However, widening the diameter in the narrow-wide structures caused a decrease in migration velocity following in direct proportion to the diameter increase ratio, whereas narrowing the diameter in wide-narrow microtunnels increased the speed without obvious correlation between velocity change and diameter change. The results demonstrated the ability of the newly developed flexible 3D gelatin tube structures for collective cell migration, and the findings provide insights into the dominant geometric factor of the emerging migratory modes for endothelial migration as asymmetric fluid flow-like behavior in the borderless cylindrical cell sheets.

Collective durotaxis of cohesive cell clusters on a stiffness gradient

Many types of motile cells perform durotaxis, namely directed migration following gradients of substrate stiffness. Recent experiments have revealed that cell monolayers can migrate toward stiffer regions even when individual cells do not-a phenomenon known as collective durotaxis. Here, we address the spontaneous motion of finite cohesive cell monolayers on a stiffness gradient. We theoretically analyze a continuum active polar fluid model that has been tested in recent wetting assays of epithelial tissues and includes two types of active forces (cell-substrate traction and cell-cell contractility). The competition between the two active forces determines whether a cell monolayer spreads or contracts. Here, we show that this model generically predicts collective durotaxis, and that it features a variety of dynamical regimes as a result of the interplay between the spreading state and the global propagation, including sequential contraction and spreading of the monolayer as it moves toward higher stiffness. We solve the model exactly in some relevant cases, which provides both physical insights into the mechanisms of tissue durotaxis and spreading as well as a variety of predictions that could guide the design of future experiments.

Photothermal Agarose Microfabrication Technology for Collective Cell Migration Analysis

Agarose photothermal microfabrication technology is one of the micropatterning techniques that has the advantage of simple and flexible real-time fabrication even during the cultivation of cells. To examine the ability and limitation of the agarose microstructures, we investigated the collective epithelial cell migration behavior in two-dimensional agarose confined structures. Agarose microchannels from 10 to 211 micrometer width were fabricated with a spot heating of a focused 1480 nm wavelength infrared laser to the thin agarose layer coated on the cultivation dish after the cells occupied the reservoir. The collective cell migration velocity maintained constant regardless of their extension distance, whereas the width dependency of those velocities was maximized around 30 micrometer width and decreased both in the narrower and wider microchannels. The single-cell tracking revealed that the decrease of velocity in the narrower width was caused by the apparent increase of aspect ratio of cell shape (up to 8.9). In contrast, the decrease in the wider channels was mainly caused by the increase of the random walk-like behavior of component cells. The results confirmed the advantages of this method: (1) flexible fabrication without any pre-designing, (2) modification even during cultivation, and (3) the cells were confined in the agarose geometry.

Hydrostatic pressure promotes migration and filamin-A activation in fibroblasts with increased p38 phosphorylation and TGF-β production

Fibroblast migration is closely regulated by the mechanical characteristics in surrounding microenvironment. While increased interstitial hydrostatic pressure (HP) is a hallmark in many pathological and physiological conditions, little is known about how the HP affects fibroblast motility. Using cell-culture chips with elevated HP conditions, we showed that 20 cmH₂O HP significantly accelerated fibroblast migration. The HP-induced migration acceleration was dependent on the augmentation of transforming growth factor-β₁, and correlated with the activation of filamin A via the phosphorylation of p38 mitogen-activated protein kinase. Our results suggest that interstitial HP elevation associated with various pathological states could significantly regulate fibroblast migration.

Distinct roles of tumor associated mutations in collective cell migration

Recent evidence suggests that groups of cells are more likely to form clinically dangerous metastatic tumors, emphasizing the importance of understanding mechanisms underlying collective behavior. The emergent collective behavior of migrating cell sheets in vitro has been shown to be disrupted in tumorigenic cells but the connection between this behavior and in vivo tumorigenicity remains unclear. We use particle image velocimetry to measure a multidimensional migration phenotype for genetically defined human breast epithelial cell lines that range in their in vivo behavior from non-tumorigenic to aggressively metastatic. By using cells with controlled mutations, we show that PTEN deletion enhances collective migration, while Ras activation suppresses it, even when combined with PTEN deletion. These opposing effects on collective migration of two mutations that are frequently found in patient tumors could be exploited in the development of novel treatments for metastatic disease. Our methods are based on label-free phase contrast imaging, and thus could easily be applied to patient tumor cells. The short time scales of our approach do not require potentially selective growth, and thus in combination with label-free imaging would allow multidimensional collective migration phenotypes to be utilized in clinical assessments of metastatic potential.

Effect of Geometric Curvature on Collective Cell Migration in Tortuous Microchannel Devices

Collective cell migration is an essential phenomenon in many naturally occurring pathophysiological processes, as well as in tissue engineering applications. Cells in tissues and organs are known to sense chemical and mechanical signals from the microenvironment and collectively respond to these signals. For the last few decades, the effects of chemical signals such as growth factors and therapeutic agents on collective cell behaviors in the context of tissue engineering have been extensively studied, whereas those of the mechanical cues have only recently been investigated. The mechanical signals can be presented to the constituent cells in different forms, including topography, substrate stiffness, and geometrical constraint. With the recent advancement in microfabrication technology, researchers have gained the ability to manipulate the geometrical constraints by creating 3D structures to mimic the tissue microenvironment. In this study, we simulate the pore curvature as presented to the cells within 3D-engineered tissue-scaffolds by developing a device that features tortuous microchannels with geometric variations. We show that both cells at the front and rear respond to the varying radii of curvature and channel amplitude by altering the collective migratory behavior, including cell velocity, morphology, and turning angle. These findings provide insights into adaptive migration modes of collective cells to better understand the underlying mechanism of cell migration for optimization of the engineered tissue-scaffold design.

Bridging the gap between single-cell migration and collective dynamics

Motivated by the wealth of experimental data recently available, we present a cellular-automaton-based modeling framework focussing on high-level cell functions and their concerted effect on cellular migration patterns. Specifically, we formulate a coarse-grained description of cell polarity through self-regulated actin organization and its response to mechanical cues. Furthermore, we address the impact of cell adhesion on collective migration in cell cohorts. The model faithfully reproduces typical cell shapes and movements down to the level of single cells, yet allows for the efficient simulation of confluent tissues. In confined circular geometries, we find that specific properties of individual cells (polarizability; contractility) influence the emerging collective motion of small cell cohorts. Finally, we study the properties of expanding cellular monolayers (front morphology; stress and velocity distributions) at the level of extended tissues.

Active matter invasion

Biologically active materials such as bacterial biofilms and eukaryotic cells thrive in confined micro-spaces. Here, we show through numerical simulations that confinement can serve as a mechanical guidance to achieve distinct modes of collective invasion when combined with growth dynamics and the intrinsic activity of biological materials. We assess the dynamics of the growing interface and classify these collective modes of invasion based on the activity of the constituent particles of the growing matter. While at small and moderate activities the active material grows as a coherent unit, we find that blobs of active material collectively detach from the cohort above a well-defined activity threshold. We further characterise the mechanical mechanisms underlying the crossovers between different modes of invasion and quantify their impact on the overall invasion speed.

Influence of proliferation on the motions of epithelial monolayers invading adherent strips

Biological systems integrate dynamics at many scales, from molecules, protein complexes and genes, to cells, tissues and organisms. At every step of the way, mechanics, biochemistry and genetics offer complementary approaches to understand these dynamics. At the tissue scale, in vitro monolayers of epithelial cells provide a model to capture the influence of various factors on the motions of the tissue, in order to understand in vivo processes from morphogenesis, cancer progression and tissue remodelling. Ongoing efforts include research aimed at deciphering the roles of the cytoskeleton, of cell-substrate and cell-cell adhesions, and of cell proliferation-the point we investigate here. We show that confined to adherent strips, and on the time scale of a day or two, monolayers move with a characteristic front speed independent of proliferation, but that the motion is accompanied by persistent velocity waves, only in the absence of cell divisions. Here we show that the long-range transmission of physical signals is strongly coupled to cell density and proliferation. We interpret our results from a kinematic and mechanical perspective. Our study provides a framework to understand density-driven mechanisms of collective cell migration.

Mathematical Models for Cell Migration with Real-Time Cell Cycle Dynamics

The fluorescent ubiquitination-based cell cycle indicator, also known as FUCCI, allows the visualization of the G1 and S/G2/M cell cycle phases of individual cells. FUCCI consists of two fluorescent probes, so that cells in the G1 phase fluoresce red and cells in the S/G2/M phase fluoresce green. FUCCI reveals real-time information about cell cycle dynamics of individual cells, and can be used to explore how the cell cycle relates to the location of individual cells, local cell density, and different cellular microenvironments. In particular, FUCCI is used in experimental studies examining cell migration, such as malignant invasion and wound healing. Here we present, to our knowledge, new mathematical models that can describe cell migration and cell cycle dynamics as indicated by FUCCI. The fundamental model describes the two cell cycle phases, G1 and S/G2/M, which FUCCI directly labels. The extended model includes a third phase, early S, which FUCCI indirectly labels. We present experimental data from scratch assays using FUCCI-transduced melanoma cells, and show that the predictions of spatial and temporal patterns of cell density in the experiments can be described by the fundamental model. We obtain numerical solutions of both the fundamental and extended models, which can take the form of traveling waves. These solutions are mathematically interesting because they are a combination of moving wavefronts and moving pulses. We derive and confirm a simple analytical expression for the minimum wave speed, as well as exploring how the wave speed depends on the spatial decay rate of the initial condition.

Dynamics phenotyping across length and time scales in collective cell migration

Processes in collective migration span many length and time scales. In this review, we focus on length scales ranging from tens of microns (single cells) to a few millimeters (cell clusters) and the motion of these cells and cell groups on time scales of minutes to hours. We focus on epithelial cell sheets and metrics of motion developed to measure migration phenotypes in this system. Comparisons between cell motion and fluid flows, facilitated by the popular image analysis technique particle image velocimetry, yield metrics that can be used to study migration across a range of length and time scales. Measuring collective cell migration across these scales provides a complex, quantitative phenotype useful for migration models, in particular those that compare and contrast collective cell migration to movement of particles near a transition to jamming. Contrasting the motion of epithelial cells and the jamming transition illustrates aspects of collective motion that can be attributed to the jammed character of cell clusters, and highlights aspects of collective behavior that likely involve active motility and cell-cell guidance. The application of multiple migration metrics, which span multiple scales of the system, thus allows us to link cell-scale signals and mechanics to collective behavior.

Pressure-driven collective growth mechanism of planar cell colonies

The growth of cell colonies is determined by the migration and proliferation of the individual cells. This is often modeled with the Fisher-Kolmogorov (FK) equation, which assumes that cells diffuse independently from each other, but stop to proliferate when their density reaches a critial limit. However, when using measured, cell-line specific parameters, we find that the FK equation drastically underestimates the experimentally observed increase of colony radius with time. Moreover, cells in real colonies migrate radially outward with superdiffusive trajectories, in contrast to the assumption of random diffusion. We demonstrate that both dicrepancies can be resolved by assuming that cells in dense colonies are driven apart by repulsive, pressure-like forces. Using this model of proliferating repelling particles (PRP), we find that colony growth exhibits different dynamical regimes, depending on the ratio between a pressure-related equilibrium cell density and the critial density of proliferation arrest.

Epithelial vertex models with active biochemical regulation of contractility can explain organized collective cell motility

Collective motions of groups of cells are observed in many biological settings such as embryo development, tissue formation, and cancer metastasis. To effectively model collective cell movement, it is important to incorporate cell specific features such as cell size, cell shape, and cell mechanics, as well as active behavior of cells such as protrusion and force generation, contractile forces, and active biochemical signaling mechanisms that regulate cell behavior. In this paper, we develop a comprehensive model of collective cell migration in confluent epithelia based on the vertex modeling approach. We develop a method to compute cell-cell viscous friction based on the vertex model and incorporate RhoGTPase regulation of cortical myosin contraction. Global features of collective cell migration are examined by computing the spatial velocity correlation function. As active cell force parameters are varied, we found rich dynamical behavior. Furthermore, we find that cells exhibit nonlinear phenomena such as contractile waves and vortex formation. Together our work highlights the importance of active behavior of cells in generating collective cell movement. The vertex modeling approach is an efficient and versatile approach to rigorously examine cell motion in the epithelium.

Tubular microscaffolds for studying collective cell migration

Epithelial cells demonstrate different collective migratory modes when encountering two (2D) and three dimensional (3D) microenvironment. While planar micropatterns and constraint have been shown to strongly impact collective cell migration (CCM), how out-of-plane curvature and 3D confinement will affect epithelial organization and dynamics remains largely unknown. This is likely due to lack of proper 3D microscaffolds for studying CCM. In this chapter, we briefly review the latest achievement in microengineering approaches to control 3D microenvironment of epithelial development. Then, we introduce convenient and simple methods of fabricating elastomeric tubular biocompatible microchannels as 3D cell culture scaffolds. Afterwards, we describe in detail the experimental set-up for observing 3D coordinated cell migration on curved surfaces and under spatial constraint. Finally, we provide an approach to analyze 3D dynamics using available techniques for 2D images.

Collective cell migration without proliferation: density determines cell velocity and wave velocity

Collective cell migration contributes to embryogenesis, wound healing and tumour metastasis. Cell monolayer migration experiments help in understanding what determines the movement of cells far from the leading edge. Inhibiting cell proliferation limits cell density increase and prevents jamming; we observe long-duration migration and quantify space-time characteristics of the velocity profile over large length scales and time scales. Velocity waves propagate backwards and their frequency depends only on cell density at the moving front. Both cell average velocity and wave velocity increase linearly with the cell effective radius regardless of the distance to the front. Inhibiting lamellipodia decreases cell velocity while waves either disappear or have a lower frequency. Our model combines conservation laws, monolayer mechanical properties and a phenomenological coupling between strain and polarity: advancing cells pull on their followers, which then become polarized. With reasonable values of parameters, this model agrees with several of our experimental observations. Together, our experiments and model disantangle the respective contributions of active velocity and of proliferation in monolayer migration, explain how cells maintain their polarity far from the moving front, and highlight the importance of strain-polarity coupling and density in long-range information propagation.

Morphology and dynamics of tumor cell colonies propagating in epidermal growth factor supplemented media

The epidermal growth factor (EGF) plays a key role in physiological and pathological processes. This work reports on the influence of EGF concentration (c _EGF) on the modulation of individual cell phenotype and cell colony kinetics with the aim of perturbing the colony front roughness fluctuations. For this purpose, HeLa cell colonies that remain confluent along the whole expansion process with initial quasi-radial geometry and different initial cell populations, as well as colonies with initial quasi-linear geometry and large cell population, are employed. Cell size and morphology as well as its adhesive characteristics depend on c _EGF. Quasi-radial colonies (QRC) expansion kinetics in EGF-containing medium exhibits a complex behavior. Namely, at the first stages of growth, the average QRC radius evolution can be described by a t ^1/2 diffusion term coupled with exponential growth kinetics up to a critical time, and afterwards a growth regime approaching constant velocity. The extension of each regime depends on c _EGF and colony history. In the presence of EGF, the initial expansion of quasi-linear colonies (QLCs) also exhibits morphological changes at both the cell and the colony levels. In these cases, the cell density at the colony border region becomes smaller than in the absence of EGF and consequently, the extension of the effective rim where cell duplication and motility contribute to the colony expansion increases. QLC front displacement velocity increases with c _EGF up to a maximum value in the 2-10 ng ml^-1 range. Individual cell velocity is increased by EGF, and an enhancement in both the persistence and the ballistic characteristics of cell trajectories can be distinguished. For an intermediate c _EGF, collective cell displacements contribute to the roughening of the colony contours. This global dynamics becomes compatible with the standard Kardar-Parisi-Zhang growth model, although a faster colony roughness saturation in EGF-containing medium than in the control medium is observed.

Emergent patterns of collective cell migration under tubular confinement

Collective epithelial behaviors are essential for the development of lumens in organs. However, conventional assays of planar systems fail to replicate cell cohorts of tubular structures that advance in concerted ways on out-of-plane curved and confined surfaces, such as ductal elongation in vivo. Here, we mimic such coordinated tissue migration by forming lumens of epithelial cell sheets inside microtubes of 1-10 cell lengths in diameter. We show that these cell tubes reproduce the physiological apical-basal polarity, and have actin alignment, cell orientation, tissue organization, and migration modes that depend on the extent of tubular confinement and/or curvature. In contrast to flat constraint, the cell sheets in a highly constricted smaller microtube demonstrate slow motion with periodic relaxation, but fast overall movement in large microtubes. Altogether, our findings provide insights into the emerging migratory modes for epithelial migration and growth under tubular confinement, which are reminiscent of the in vivo scenario.

Jamming transitions in cancer

The traditional picture of tissues, where they are treated as liquids defined by properties such as surface tension or viscosity has been redefined during the last few decades by the more fundamental question: under which conditions do tissues display liquid-like or solid-like behaviour? As a result, basic concepts arising from the treatment of tissues as solid matter, such as cellular jamming and glassy tissues, have shifted into the current focus of biophysical research. Here, we review recent works examining the phase states of tissue with an emphasis on jamming transitions in cancer. When metastasis occurs, cells gain the ability to leave the primary tumour and infiltrate other parts of the body. Recent studies have shown that a linkage between an unjamming transition and tumour progression indeed exists, which could be of importance when designing surgery and treatment approaches for cancer patients.

Hydrodynamic instabilities, waves and turbulence in spreading epithelia

We present a hydrodynamic model of spreading epithelial monolayers described as polar viscous fluids, with active contractility and traction on a substrate. The combination of both active forces generates an instability that leads to nonlinear traveling waves, which propagate in the direction of polarity with characteristic time scales that depend on contact forces. Our viscous fluid model provides a comprehensive understanding of a variety of observations on the slow dynamics of epithelial monolayers, remarkably those that seemed to be characteristic of elastic media. The model also makes simple predictions to test the non-elastic nature of the mechanical waves, and provides new insights into collective cell dynamics, explaining plithotaxis as a result of strong flow-polarity coupling, and quantifying the non-locality of force transmission. In addition, we study the nonlinear regime of waves deriving an exact map of the model into the complex Ginzburg-Landau equation, which provides a complete classification of possible nonlinear scenarios. In particular, we predict the transition to different forms of weak turbulence, which in turn could explain the chaotic dynamics often observed in epithelia.

Collective cell migration: a physics perspective

Cells have traditionally been viewed either as independently moving entities or as somewhat static parts of tissues. However, it is now clear that in many cases, multiple cells coordinate their motions and move as collective entities. Well-studied examples comprise development events, as well as physiological and pathological situations. Different ex vivo model systems have also been investigated. Several recent advances have taken place at the interface between biology and physics, and have benefitted from progress in imaging and microscopy, from the use of microfabrication techniques, as well as from the introduction of quantitative tools and models. We review these interesting developments in quantitative cell biology that also provide rich examples of collective out-of-equilibrium motion.

Modeling collective cell migration in geometric confinement

Monolayer expansion has generated great interest as a model system to study collective cell migration. During such an expansion the culture front often develops 'fingers', which we have recently modeled using a proposed feedback between the curvature of the monolayer's leading edge and the outward motility of the edge cells. We show that this model is able to explain the puzzling observed increase of collective cellular migration speed of a monolayer expanding into thin stripes, as well as describe the behavior within different confining geometries that were recently observed in experiments. These comparisons give support to the model and emphasize the role played by the edge cells and the edge shape during collective cell motion.

Physical models of collective cell motility: from cell to tissue

In this article, we review physics-based models of collective cell motility. We discuss a range of techniques at different scales, ranging from models that represent cells as simple self-propelled particles to phase field models that can represent a cell's shape and dynamics in great detail. We also extensively review the ways in which cells within a tissue choose their direction, the statistics of cell motion, and some simple examples of how cell-cell signaling can interact with collective cell motility. This review also covers in more detail selected recent works on collective cell motion of small numbers of cells on micropatterns, in wound healing, and the chemotaxis of clusters of cells.

Effective viscosity and dynamics of spreading epithelia: a solvable model

Collective cell migration in spreading epithelia in controlled environments has become a landmark in our current understanding of fundamental biophysical processes in development, regeneration, wound healing or cancer. Epithelial monolayers are treated as thin layers of a viscous fluid that exert active traction forces on the substrate. The model is exactly solvable and shows a broad range of applicabilities for the quantitative analysis and interpretation of force microscopy data of monolayers from a variety of experiments and cell lines. In addition, the proposed model provides physical insights into how the biological regulation of the tissue is encoded in a reduced set of time-dependent physical parameters. In particular the temporal evolution of the effective viscosity entails a mechanosensitive regulation of adhesion. Besides, the observation of an effective elastic tensile modulus can be interpreted as an emergent phenomenon in an active fluid.

Inference of Internal Stress in a Cell Monolayer

We combine traction force data with Bayesian inversion to obtain an absolute estimate of the internal stress field of a cell monolayer. The method, Bayesian inversion stress microscopy, is validated using numerical simulations performed in a wide range of conditions. It is robust to changes in each ingredient of the underlying statistical model. Importantly, its accuracy does not depend on the rheology of the tissue. We apply Bayesian inversion stress microscopy to experimental traction force data measured in a narrow ring of cohesive epithelial cells, and check that the inferred stress field coincides with that obtained by direct spatial integration of the traction force data in this quasi one-dimensional geometry.

Multiscale Cues Drive Collective Cell Migration

To investigate complex biophysical relationships driving directed cell migration, we developed a biomimetic platform that allows perturbation of microscale geometric constraints with concomitant nanoscale contact guidance architectures. This permits us to elucidate the influence, and parse out the relative contribution, of multiscale features, and define how these physical inputs are jointly processed with oncogenic signaling. We demonstrate that collective cell migration is profoundly enhanced by the addition of contract guidance cues when not otherwise constrained. However, while nanoscale cues promoted migration in all cases, microscale directed migration cues are dominant as the geometric constraint narrows, a behavior that is well explained by stochastic diffusion anisotropy modeling. Further, oncogene activation (i.e. mutant PIK3CA) resulted in profoundly increased migration where extracellular multiscale directed migration cues and intrinsic signaling synergistically conspire to greatly outperform normal cells or any extracellular guidance cues in isolation.

Collective Signal Processing in Cluster Chemotaxis: Roles of Adaptation, Amplification, and Co-attraction in Collective Guidance

Single eukaryotic cells commonly sense and follow chemical gradients, performing chemotaxis. Recent experiments and theories, however, show that even when single cells do not chemotax, clusters of cells may, if their interactions are regulated by the chemoattractant. We study this general mechanism of "collective guidance" computationally with models that integrate stochastic dynamics for individual cells with biochemical reactions within the cells, and diffusion of chemical signals between the cells. We show that if clusters of cells use the well-known local excitation, global inhibition (LEGI) mechanism to sense chemoattractant gradients, the speed of the cell cluster becomes non-monotonic in the cluster's size-clusters either larger or smaller than an optimal size will have lower speed. We argue that the cell cluster speed is a crucial readout of how the cluster processes chemotactic signals; both amplification and adaptation will alter the behavior of cluster speed as a function of size. We also show that, contrary to the assumptions of earlier theories, collective guidance does not require persistent cell-cell contacts and strong short range adhesion. If cell-cell adhesion is absent, and the cluster cohesion is instead provided by a co-attraction mechanism, e.g. chemotaxis toward a secreted molecule, collective guidance may still function. However, new behaviors, such as cluster rotation, may also appear in this case. Co-attraction and adaptation allow for collective guidance that is robust to varying chemoattractant concentrations while not requiring strong cell-cell adhesion.

Ring-Shaped Microlanes and Chemical Barriers as a Platform for Probing Single-Cell Migration

Quantification and discrimination of pharmaceutical and disease-related effects on cell migration requires detailed characterization of single-cell motility. In this context, micropatterned substrates that constrain cells within defined geometries facilitate quantitative readout of locomotion. Here, we study quasi-one-dimensional cell migration in ring-shaped microlanes. We observe bimodal behavior in form of alternating states of directional migration (run state) and reorientation (rest state). Both states show exponential lifetime distributions with characteristic persistence times, which, together with the cell velocity in the run state, provide a set of parameters that succinctly describe cell motion. By introducing PEGylated barriers of different widths into the lane, we extend this description by quantifying the effects of abrupt changes in substrate chemistry on migrating cells. The transit probability decreases exponentially as a function of barrier width, thus specifying a characteristic penetration depth of the leading lamellipodia. Applying this fingerprint-like characterization of cell motion, we compare different cell lines, and demonstrate that the cancer drug candidate salinomycin affects transit probability and resting time, but not run time or run velocity. Hence, the presented assay allows to assess multiple migration-related parameters, permits detailed characterization of cell motility, and has potential applications in cell biology and advanced drug screening.

In vivo confinement promotes collective migration of neural crest cells

Collective cell migration is fundamental throughout development and in many diseases. Spatial confinement using micropatterns has been shown to promote collective cell migration in vitro, but its effect in vivo remains unclear. Combining computational and experimental approaches, we show that the in vivo collective migration of neural crest cells (NCCs) depends on such confinement. We demonstrate that confinement may be imposed by the spatiotemporal distribution of a nonpermissive substrate provided by versican, an extracellular matrix molecule previously proposed to have contrasting roles: barrier or promoter of NCC migration. We resolve the controversy by demonstrating that versican works as an inhibitor of NCC migration and also acts as a guiding cue by forming exclusionary boundaries. Our model predicts an optimal number of cells in a given confinement width to allow for directional migration. This optimum coincides with the width of neural crest migratory streams analyzed across different species, proposing an explanation for the highly conserved nature of NCC streams during development.

Collective cell migration over long time scales reveals distinct phenotypes

Introduction

Migratory phenotypes of metastasizing tumor cells include single and collective cell migration. While migration of tumor cells is generally less cooperative than that of normal epithelial cells, our understanding of precisely how they differ in long time behavior is incomplete.

Objectives

We measure in a model system how cancer progression affects collective migration on long time scales, and determine how perturbation of cell-cell adhesions, specifically reduced E-cadherin expression, affects the collective migration phenotype.

Methods

Time lapse imaging of cellular sheets and particle image velocimetry (PIV) are used to quantitatively study the dynamics of cell motion over ten hours. Long time dynamics are measured via finite time Lyapunov exponents (FTLE) and changes in FTLE with time.

Results

We find that non-malignant MCF10A cells are distinguished from malignant MCF10CA1a cells by both their short time (minutes) and long time (hours) dynamics. In addition, short time dynamics distinguish non-malignant E-cadherin knockdown cells from the control, but long time dynamics and increasing spatial correlations remain unchanged.

Discussion

Epithelial sheet collective behavior includes long time dynamics that cannot be captured by metrics that assess cooperativity based on short time dynamics, such as instantaneous speed or directionality. The use of metrics incorporating migration data over hours instead of minutes allows us to more precisely describe how E-cadherin, a clinically relevant adhesion molecule, affects collective migration. We predict that the long time scale metrics described here will be more robust and predictive of malignant behavior than analysis of instantaneous velocity fields alone.

One-dimensional collective migration of a proliferating cell monolayer

The importance of collective cellular migration during embryogenesis and tissue repair asks for a sound understanding of underlying principles and mechanisms. Here, we address recent in vitro experiments on cell monolayers, which show that the advancement of the leading edge relies on cell proliferation and protrusive activity at the tissue margin. Within a simple viscoelastic mechanical model amenable to detailed analysis, we identify a key parameter responsible for tissue expansion, and we determine the dependence of the monolayer velocity as a function of measurable rheological parameters. Our results allow us to discuss the effects of pharmacological perturbations on the observed tissue dynamics.

Physics of active jamming during collective cellular motion in a monolayer

Although collective cell motion plays an important role, for example during wound healing, embryogenesis, or cancer progression, the fundamental rules governing this motion are still not well understood, in particular at high cell density. We study here the motion of human bronchial epithelial cells within a monolayer, over long times. We observe that, as the monolayer ages, the cells slow down monotonously, while the velocity correlation length first increases as the cells slow down but eventually decreases at the slowest motions. By comparing experiments, analytic model, and detailed particle-based simulations, we shed light on this biological amorphous solidification process, demonstrating that the observed dynamics can be explained as a consequence of the combined maturation and strengthening of cell-cell and cell-substrate adhesions. Surprisingly, the increase of cell surface density due to proliferation is only secondary in this process. This analysis is confirmed with two other cell types. The very general relations between the mean cell velocity and velocity correlation lengths, which apply for aggregates of self-propelled particles, as well as motile cells, can possibly be used to discriminate between various parameter changes in vivo, from noninvasive microscopy data.

Emergence and Persistence of Collective Cell Migration on Small Circular Micropatterns

The spontaneous formation of vortices is a hallmark of collective cellular activity. Here, we study the onset and persistence of coherent angular motion as a function of the number of cells N confined in circular micropatterns. We find that the persistence of coherent angular motion increases with N but exhibits a pronounced discontinuity accompanied by a geometric rearrangement of cells to a configuration containing a central cell. Computer simulations based on a generalized Potts model reproduce the emergence of vortex states and show in agreement with experiment that their stability depends on the interplay of the spatial arrangement and internal polarization of neighboring cells. Hence, the distinct migrational states in finite size ensembles reveal significant insight into the local interaction rules guiding collective migration.

Phenomenological approaches to collective behavior in epithelial cell migration

Collective cell migration in epithelial tissues resembles fluid-like behavior in time-lapse recordings. In the last years, hydrodynamic velocity fields in living matter have been studied intensely. The emergent properties were remarkably similar to phenomena known from active soft matter systems. Here, we review migration experiments of large cellular ensembles as well as of mesoscopic cohorts in micro-structured environments. Concepts such as diffusion, velocity correlations, swirl strength and polarization are metrics to quantify the cellular dynamics both in experiments as well as in computational simulations. We discuss challenges relating collective migration to single cell and oligocellular behavior as well as linking the phenotypic parameters to the underlying cytoskeleton dynamics and signaling networks. This article is part of a Special Issue entitled: Mechanobiology.

Architecture and migration of an epithelium on a cylindrical wire

In a wide range of epithelial tissues such as kidney tubules or breast acini, cells organize into bidimensional monolayers experiencing an out-of-plane curvature. Cancer cells can also migrate collectively from epithelial tumors by wrapping around vessels or muscle fibers. However, in vitro experiments dealing with epithelia are mostly performed on flat substrates, neglecting this out-of-plane component. In this paper, we study the development and migration of epithelial tissues on glass wires of well-defined radii varying from less than 1 µm up to 85 µm. To uncouple the effect of out-of-plane curvature from the lateral confinement experienced by the cells in these geometries, we compare our results to experiments performed on narrow adhesive tracks. Because of lateral confinement, the velocity of collective migration increases for radii smaller than typically 20 µm. The monolayer dynamics is then controlled by front-edge protrusions. Conversely, high curvature is identified as the inducer of frequent cell detachments at the front edge, a phenotype reminiscent of the Epithelial-Mesenchymal Transition. High curvature also induces a circumferential alignment of the actin cytoskeleton, stabilized by multiple focal adhesions. This organization of the cytoskeleton is reminiscent of in vivo situations such as the development of the trachea of the Drosophila embryo. Finally, submicron radii halt the monolayer, which then reconfigures into hollow cysts.